10
votes
Accepted
How to correct underdispersion in logistic regression
Getting a residual mean deviance around 0.63 is perfectly normal for binary regression and it does not indicate underdispersion or overdispersion. For binary regression, the residual deviance is ...
- 13.5k
7
votes
Modelling count data with extreme underdispersion - what distribution?
The Conway-Maxwell-Poisson model has recently been shown to handle arbitrarily small underdispersion (see Huang 2020). For example, it is possible to have a mean of 15 and a variance of 2, say, by ...
- 71
6
votes
Accepted
Quasi-poisson for underdispersed data
Quasi-likelihood theory is as valid with underdispersed data as it is with overdispersed data, so you could just go that way.
But, I would be careful, context matters a lot. While overdispersion is ...
- 82.8k
5
votes
Accepted
Is there a common underdispersed discrete distribution with unbounded support for general mean and variance?
The Conway-Maxwell-Poisson distribution (https://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution) has unbounded support (on the right) and can model both under- and over-...
- 41.1k
4
votes
Does binomial distribution have the smallest possible variance among all "reasonable" distributions that can model binary elections?
Double-no (it maximises the variance)
The answer from whuber is excellent. To supplement that answer, it is also worth examining what happens if you assume that the votes are independent. If we take ...
- 133k
4
votes
What is the appropriate model for underdispersed count data?
It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only ...
- 61
4
votes
Accepted
Count process with standard deviation proportional to its mean
Mean-variance relationships are defined for families of probability distributions, especially families indexed by a single parameter.
As we vary the unknown parameter, both the mean and the variance ...
- 13.5k
3
votes
From overdispersion to underdispersion: comparing linear regression models with DHARMa
What Ben says but also:
What I mainly see in your plots is a distributional misfit (wiggle in qq plot) and autocorrelation. The underdispersion is likely a secondary problem.
The misfit is not ...
- 8,699
3
votes
From overdispersion to underdispersion: comparing linear regression models with DHARMa
The most common overdispersion tests in the literature — comparing (resid deviance)/(resid df) to 1, or (sum of [Pearson resids]^2)/(resid df) to 1, or computing the one-tailed p-value of resid ...
- 47.3k
3
votes
Residual Deviance and degrees of freedom - Negative Binomial Distribution
For modelling count data in regression settings, the negative binomial GLM is far preferable to the Poisson GLM. Indeed, I would go so far as to say that the latter is a bad model that should almost ...
- 133k
3
votes
Accepted
Causes for Underdispersion in Poisson Regression
Undispersion might not be a surprise in this case. From a comment by @Ben Bolker: Suppose (for example) a particular woman has a conditional expected number of pregnancies equal to 1. Density of ...
- 82.8k
3
votes
Accepted
How different from one does a dispersion ratio have to be to be considered significant?
No, there is no universal rule of thumb for this, and you should definitey not rely on p values. If you have reason to think that you have over or under dispersion, then go ahead and fit a model that ...
- 65.8k
3
votes
Accepted
Zero-inflated generalized Poisson mixed effect model with glmmTMB still zero inflated
I'm the developer of DHARMa. This is a fairly specific question and it's hard to say definite things from the distance, but I would like to supply a few thoughts:
Underdispersion is fairly uncommon ...
- 8,699
3
votes
Overdispersion and Underdispersion in Negative Binomial/Poisson Regression
No, it doesn't --- it means a good fit (with some caveats)
In this context, the Pearson chi-squared test is used to assess the goodness of fit of the estimated distribution under your assumed model ...
- 133k
2
votes
Index of Dispersion - How to test its significance?
If you look at your first link, Index of Dispersion, under the "Statistics" section, it says (see Wikipedia link for definitions)
If the variates are Poisson distributed then the index of ...
- 13.1k
2
votes
What does the dispersion parameter mean in negative binomial regression?
If you are using glm.nb from the MASS package, the variance is $\mu+\mu^2/\theta$, so the variance is larger than $\mu$. Different packages may define the dispersion parameter differently. But, if it ...
- 2,652
2
votes
Explanation and simulation of under-dispersion in quasi poisson GLM
I was wondering what the explanation of this under dispersion might be
A Poisson distribution can describe events happening independently over time. The variance of Poisson-distributed counts among ...
- 102k
2
votes
Dispersion parameter in DHARMA
The default dispersion parameter estimated by DHARMa is essentially observed/expected variance, so 0.8 means that there is 20% lower variance than expected, which I would consider a small to moderate ...
- 8,699
1
vote
Are overdispersion and underdispersion in a binomial logistic regression model an issue if the model is not being used to make predictions?
Yes, it certainly is an issue. If you use hypothesis tests on the coefficients, and there is overdispersion, but you don't account for it: Some coefficients might be significantly different from zero,...
- 82.8k
1
vote
Is underdispersion problemetic for predictive poisson models?
If you are only interested in the predictions, then a Poisson regression model and a quasiPoisson regression model gives identical predictions, whether there are under- or over-dispersion.
The ...
- 82.8k
1
vote
Issues with Conway Maxwell Poisson Family in glmmTMB
There are several problems here:
COM-Poisson evaluation is inherently slow, because the normalization constant has to be evaluated by brute-force summation;
COM-Poisson is especially slow when the ...
- 47.3k
1
vote
Is my variance compatible with a Poisson distribution
This is a case of underdispersion, where the observed data is less variable than the model allows. As a distribution with only one parameters, the Poisson can only model one relationship between the ...
- 1,069
1
vote
How to address underdispersion in a GLMM
I do not understand why you believe there is anything to fix. The dispersion of a Gaussian GLM is simply the sum of squares divided by the residual degrees of freedom (see ...
- 7,086
1
vote
Sampling from under/over-dispersed count data in R
Simulating on the continuum from not overdispersed to over-dispersed is easy: you fix a rate $\lambda$ (no overdispersion) or you draw your rates from a gamma distribution (=overdispersion). This is ...
- 35.2k
1
vote
How to define the nu parameter of Conway-Maxwell-Poisson in spaMM package
The dispersion parameter of the COMPoisson can be estimated by using the fitme function instead of HLfit, as shown in the first example of the documentation page partially reproduced in the OP.
- 11
1
vote
Modeling count data with underdispersion
You can use a glm model with a quassipoisson family which relaxes the relationship between variance and mean. For the Poisson regression this is $VAR[X] = E[X]$, the variance is equal to the mean. For ...
- 86.5k
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